To find the score for the last game that will give Carlos an average of 25 points per game, we can use the following approach:
First, we need to sum the points scored in the first 6 games:
\(27 + 18 + 24 + 32 + 15 + 27 = 143\)
Next, let \(s\) be the score for the last game. The total number of games played when including the last game is 7. To average 25 points over 7 games, the equation can be set up as:
\[ \frac{143 + s}{7} = 25 \]
Now, we can multiply both sides by 7 to eliminate the fraction:
\[ 143 + s = 175 \]
This implies:
\[ s = 175 - 143 \] \[ s = 32 \]
Now looking at the response options:
A. \( \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \)
B. \( \frac{27 + 18 + 24 + 32 + 15 + 17 + s}{7} = 25 \)
C. \( \frac{27 + 18 + 24 + 32 + 15 + 27 + s}{7} = 25 \)
D. \( \frac{143 + s}{7} = 25 \)
The correct choices that accurately express the situation are A and C, as both properly set up the average calculation with the sum of his scores plus the unknown score \(s\) divided by the total number of games, which is 7.
Option D is also accurate since it reflects the sum directly but in relation to the average formula.
So, the best ways to express the situation are A, C, and D.
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